Figure REF (c) shows that \(L_H\)  in the \(\mbox{\textit {Fr}}= 2\)  spheroid wake contracts in the region \(5 < x < 30\)  as a response to the expansion of \(L_V\)  (figure REF a) by steady lee waves. This phenomenon leads to the `butterfly' shaped structure of mean \(U_x\)  (figure REF (d,e)) which was also observed at a lower Reynolds number, \(=10^4\)  in [1]}. In that study, which was performed at \(= 10^4\) , the spheroid wake at critical \(\mbox{\textit {Fr}}_c\)  relaminarized. Here, at a higher \(= 10^{5}\) , the flow response at the resonant state is quite different. The constriction of \(L_H\)  leads to an enhancement in the mean horizontal shear shown in figure REF (f). This enhancement significantly slows down the decay of horizontal production (figure REF b). While \(\varepsilon \)  continues to decay, \(\lbrace P\rbrace /\lbrace \varepsilon \rbrace \)  becomes \(>1\)  leading to an increase of TKE for \(x >40\)  (figure REF a). In figure REF (d-f), we also see the maximum TKE location moving to the wake axis from its off-center location in the near wake. It is worth noting that the enhanced \(\lbrace P\rbrace \)  that acts as a source of TKE is a sink for the mean energy. The sharp increase in TKE leads to a faster decay of \(U_d\) , and the \(\mbox{\textit {Fr}}=2\)  wake transitions to the Q2D regime early on, at \(x \approx 40\) .
